Rings with finite decomposition of identity
A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semid...
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| Datum: | 2011 |
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Інститут математики НАН України
2011
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| Schriftenreihe: | Український математичний журнал |
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/166010 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Rings with finite decomposition of identity / M.A. Dokuchaev, N.M. Gubareni, V.V. Kirichenko // Український математичний журнал. — 2011. — Т. 63, № 3. — С. 319–340. — Бібліогр.: 48 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1660102025-02-23T18:40:37Z Rings with finite decomposition of identity Кiльця iз скiнченним розкладом одиницi Dokuchaev, M.A. Gubareni, N.M. Kirichenko, V.V. Статті A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semidistributive semiperfect ring is distributive. An application of decompositions of identity to groups of units is given. Наведено критерiй первинностi напiвпервинних кiлець iз скiнченним розкладом одиницi, а також короткий огляд деяких умов скiнченностi вiдносно розкладу одиницi. Розглянуто поняття сiтки кiльця i показано, що решiтка всiх двобiчних iдеалiв правого напiвдистрибутивного напiвдосконалого кiльця є дистрибутивною. Наведено застосування розкладу одиницi до груп одиниць. 2011 Article Rings with finite decomposition of identity / M.A. Dokuchaev, N.M. Gubareni, V.V. Kirichenko // Український математичний журнал. — 2011. — Т. 63, № 3. — С. 319–340. — Бібліогр.: 48 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/166010 512.5 en Український математичний журнал application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Статті Статті |
| spellingShingle |
Статті Статті Dokuchaev, M.A. Gubareni, N.M. Kirichenko, V.V. Rings with finite decomposition of identity Український математичний журнал |
| description |
A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semidistributive semiperfect ring is distributive. An application of decompositions of identity to groups of units is given. |
| format |
Article |
| author |
Dokuchaev, M.A. Gubareni, N.M. Kirichenko, V.V. |
| author_facet |
Dokuchaev, M.A. Gubareni, N.M. Kirichenko, V.V. |
| author_sort |
Dokuchaev, M.A. |
| title |
Rings with finite decomposition of identity |
| title_short |
Rings with finite decomposition of identity |
| title_full |
Rings with finite decomposition of identity |
| title_fullStr |
Rings with finite decomposition of identity |
| title_full_unstemmed |
Rings with finite decomposition of identity |
| title_sort |
rings with finite decomposition of identity |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| topic_facet |
Статті |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/166010 |
| citation_txt |
Rings with finite decomposition of identity / M.A. Dokuchaev, N.M. Gubareni, V.V. Kirichenko // Український математичний журнал. — 2011. — Т. 63, № 3. — С. 319–340. — Бібліогр.: 48 назв. — англ. |
| series |
Український математичний журнал |
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2025-11-24T11:38:45Z |
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